Electronic copy available at: http://ssrn.com/abstract=2587282

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Market Making and Risk Management in Options Markets

Naomi E. Boyd

Department of Finance, West Virginia University, Morgantown, WV 26505, USA

Abstract

This article examines the personal trading strategies of member proprietary traders in the

natural gas futures options market. Trading activity is found to mirror previous findings in

futures markets, specifically high frequency trading, with low risk exposure. The portfolio of

risk holdings by member proprietary traders are also examined to identify whether they are

instantaneously hedged using the underlying futures market, as well as to investigate how

they manage their inventory holding, rebalancing, and volatility risk exposures. Findings of

longer-term risk management practices by option markets indicate that instantaneous hedging

does not take place in this market. Exposure to price and volatility risks is actively managed,

while rebalancing risk exposure has a significant impact on profit for this trading group.

I would like to thank Peter Locke for his invaluable insights and comments, Li Sun, participants of the 2008

Financial Management Association doctoral consortium, the 2009 Financial Management Association and

Southern Finance Association meetings, seminar participants from West Virginia University, Kansas State

University, Clemson University and the University of Rhode Island for their helpful comments.

Naomi Boyd was a Consultant, Office of Chief Economist, Commodity Futures Trading Commission (CFTC),

Washington, D.C. when this research was conducted. The ideas expressed in this paper are those of the authors

and do not necessarily reflect those of Commodity Futures Trading Commission or its staff.

* Corresponding author: Tel.: +1-304-293-7891; fax: +1-304-293-5652.

Electronic copy available at: http://ssrn.com/abstract=2587282

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INTRODUCTION

The services of liquidity production and price determination that market makers provide

serve a vital role in the proper and orderly functioning of the aggregate financial market system.

Without the presence of market makers, the system would be less efficient and more costly to

maintain. How and why market makers provide these services should be influenced by the

structure under which they operate. Market makers can be categorized within two central

structures: (1) a designated structure under which the market maker has an assigned role and is

obligated to perform certain duties including, but not limited to, providing liquidity, filling

orders, setting prices, and maintaining price continuity or (2) an open structure under which a

market maker is governed only by the rules set forth by the exchange for all traders.

U.S. futures options (commodity options) operate under an open trading structure which

mimics the futures trading architecture, where members may broker orders or trade for their own

accounts with little constraint on their trading strategies. Floor traders (or their screen trading

equivalents) who choose to make a market with their trading are not required to maintain

inventory or price continuity and can enter and exit the market freely and without constraint,

other than risk controls imposed by their brokerage account. They have no privileged access to

pending orders, but at least on the floor have first-hand observation of trading activity and the

shouting and gesturing which predate a trade. Each trade must be categorized as a trade for the

executing members own account, the member’s clearing firm account, another member’s own

account, or a non-member account (customer). A member’s income can be derived from

proprietary trading and brokerage.

Research on futures markets has established that member proprietary trading serves the

market-making function in futures markets with trading behavior that is characterized by low

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end-of-day inventory holdings, small trades, and large volumes (Silber 1984, Kuserk and Locke,

1993, 1994). Related work shows highly volatile, short run profitability to futures proprietary

trading (Locke and Mann 2005). Proprietary options’ trading in natural gas futures options is

examined here to describe the institutional details of option market maker behavior.

It is shown that member proprietary trading in futures-options markets serves the market-

making function just as was previously documented by Kuserk and Locke (1993) in the

corresponding futures markets. This finding documents one of the many similarities between

how these markets operate. Member proprietary traders are characterized by their small trade

sizes, high volumes, small amount of time between trades, and low end-of-day inventory levels.

These characteristics are indicative of a market maker performing the tasks of providing liquidity

and price setting. This analysis also shows that these traders are profitable on average, albeit at

very low levels. Therefore, market making is a viable, profitable trading strategy for these

traders.

Since there is an active group of market makers in the futures market supplying liquidity

and making that market, futures options market makers would not benefit from similarly making

a market indirectly in the futures price. Instead, as Figlewski (1989) points out, a trader making a

market in options will benefit from eliminating futures price risk and concentrating on the other

risk factors. Trading options, unlike futures, involves more than univariate risk management. In

addition to exposure to changes in the futures price, the option value is also affected by changes

in the other factors which influence the option value, most notably the expectation of futures

price volatility. Management of the exposure to the futures price can be easily accomplished by

trading futures. Management of the exposure to volatility which arises in options trading requires

trading in other options. In terms of common option parameters, delta represents the exposure to

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futures price risk, and vega represents exposure to volatility risk1. If option market makers use

the underlying futures market to hedge away their exposure to price risk, they could strategically

manage their residual risk and potentially earn higher profits than those who chose other trading

strategies.

In particular, we focus on the risks taken by proprietary traders, in terms of sensitivities

to parameters in an option pricing model. The manner in which these traders manage the various

risks allow us to infer market making as a strategy and describe particular characteristics of that

strategy. We focus on the ability of option market makers to dispel inventory holding risk

through simultaneous participation in the underlying futures market. The hedging practices of

market makers have been shown to reduce the costs of providing liquidity (Çetin, Protter, and

Warachka, 2006) as well as have been shown to have a direct impact on the size of bid-ask

spreads in option markets (Huh et. al. 2012). Thus, how option market markets hedge has direct

implications into market frictions such as transactions costs which will influence the price setting

practices of these traders. We also evaluate these traders exposure to gamma and vega risk to

examine whether they maintain level or changing levels of risk throughout the trading day on

average.

This paper is the first known study to attempt to formally and empirically test the theories

posited by Figlewski (1989) and Cox & Rubinstein (1985) that option traders maintain delta

neutral positions by establishing corresponding and offsetting trades in the underlying futures

market. Thus, it is thought that option market makers engage in hedging by (for example)

purchasing a quantity of futures options while simultaneously executing a certain number of

1 For example, if the delta of an option is .5, then a $.10 change in the futures price will lead to an approximately

$.05 change in the option value, holding all else constant. By selling one futures contract for every two options

contracts, this will temporarily eliminate the futures price. The residual risk would be the other option pricing

factors, such as volatility.

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contracts in the underlying futures contract, seeking instantaneous delta neutrality. The degree to

which these traders hedge by participating in both markets will determine their vulnerability to

the risk of holding positions in the option market. The short-run exposure of the futures-option

market maker to price risk, delta, is expected to be small if they are instantaneously delta-hedged

while the exposure to volatility, vega, may more accurately represent the “inventory” that the

market maker is carrying.

We find that futures-option market makers hedging practices do not coincide with

instantaneous hedging. Rather, their use of the underlying futures markets reflects a longer term

price risk management strategy. This type of strategy would be driven by option market makers

utilizing the underlying futures market to hedge when they cannot easily liquidate their inventory

in the options market or when they wish to hold onto a position for an extended period of time

(intraday) to allow prices to equilibrate or move into profitable territory. We also note that large

traders actively seek to hedge using the futures markets, which is in line with their

correspondingly larger inventory holdings; while smaller traders tend to keep most of their

trading centralized in the option market. On average, futures-option market makers maintain very

low levels of price risk over the course of a trading day while their levels of rebalancing risk and

volatility risk are much higher. Thus, futures-option market makers’ primary exposure is to

gamma and vega, or the speed at which delta changes in response to a change in the underlying

futures price and the response of the option price to a change in the volatility of the futures price,

respectively. In fact, analysis the impact of the three risk parameters on daily profits reveals that

gamma risk has the most substantial impact on the profitability of an option market maker.

The remainder of this article is organized as follows: Section II provides information

regarding the data; Section III investigates the behavior of market makers in options markets

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through a descriptive analysis; Section IV analyzes how market makers hedge their exposure to

price risk as well as details their intraday rebalancing and volatility risk exposures in the option

market; Section V concludes.

II. DATA

The data for this research consist of 20 months of transaction-level data in the natural-gas

futures and futures option markets traded on NYMEX (now part of the CME group), spanning

September 2005 through April 2007. This data set is maintained by the U.S. Commodity Futures

Trading Commission and comes from the computerized trade reconstruction (CTR) records

compiled and maintained by the agency from data feeds from the exchanges.

Trading rules specify the obligations of the floor traders and how trades are to be

executed and recorded. When trades are executed on the floor, the trader on the sale side, for

either a futures or futures option, reports the transaction to the exchange for clearing. The

exchange records the relevant information regarding which futures or options expiration is

traded, the price or option premium, strike price, and information about the counterparties. The

information also requires an indication by the broker as to whether the trade was for a proprietary

account, another floor trader, the traders clearing member, or some outside customer.

Our dataset includes the records of all options floor trades and provides information

including the price, quantity of the trade, trade date, trade time to the second, trade direction (buy

or sell), delivery month and year of the contract, customer type (trade for the member’s account,

his or her house’s account, another member on the floor, or a customer), counterparty’s customer

type, and the floor trader’s identification. We also use corresponding futures and options daily

settlement prices and daily interest rates (3-month T-bill).

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As in previous research in this area, traders who executed personal options trades

infrequently are removed from the sample. We calculate a measure of incumbency as the

percentage of all possible days that each trader executed proprietary trades, and drop those

traders who participated on 5% or less of the days, reducing the number of options traders from

144 to 91.

Natural gas futures and options trade in the physical environment from 9:00 am to 2:30

pm (ET). The futures contracts trade in units of 10,000 British thermal units (mmBtu) and

contracts which are not eventually offset require physical settlement. The minimum price

fluctuation is $0.001 per mmBtu, or $10 per contract. Typical natural gas prices range from $5 to

$15 per 10,000 mmBTU, yielding a notional contract value of $50,000 to $150,000 dollars.

When delivery does occur it is a throughput at the Sabine Pipe Line Company’s Henry

Hub in Louisiana. This can take place no earlier than the first calendar day of the delivery month

and no later than the last calendar day of the delivery month. The Henry Hub is a many natural-

gas pipelines that serve markets throughout the U.S. east coast, the Gulf and the Gulf Coast, and

the Midwest up to the Canadian border. The futures seller is responsible for the movement of the

gas through the Hub and pays all Hub fees while the buyer is responsible for movement from the

Hub.

III. MARKET MAKER TRADING STRATEGIES

We follow previous research by Working (1967, 1977), Silber (1984), and Kuserk and

Locke (1993, 1994) to examine whether traders carrying out member proprietary trades take on

the role of market makers within the competitive framework of an option market. Due to the link,

both institutionally and through arbitrage conditions, of the futures and futures-options markets,

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it is an empirical question as to whether the characteristics of market makers in futures markets

universally hold in the option market.

A. Market Making Activity

The positions and levels of market-making activity are determined through an

examination of several variables that have been shown to distinguish market makers from other

types of floor traders in the futures market. These descriptive statistics for active, proprietary

traders over the first three nearest contract months for options are provided in Table 1, Panel A.

Total trades documents how many different transactions were entered into over the sample

period. Similarly, total contracts are the total option contracts bought by these traders. The

average time between trades is calculated by first taking the average number of minutes between

each trade each day, and then averaging this number across trader days. There are a total of

15,573 trader days in the sample, for our 91 traders over the 413 of days in the sample. As is

shown in Panel A, on average option proprietary trading is similar to that of proprietary trading

in futures markets: traders maintain relatively low levels of inventory and provide liquidity

services to the market by trading frequently, in small amounts, with high levels of overall

volume.

[Insert Table 1 about here]

B. Market Making Revenue

Member proprietary trader’s income can be derived from proprietary trading and

brokerage. While the analysis that follows is meant to show whether member proprietary trading

generates positive levels of income for the trader on average, certain macroeconomic and market

specific factors may also influence the level of income during certain time periods. For example,

the relationship between commodity-equity cross-market linkages could drive profitability for

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traders. This issue was examined by Buyuksahin and Robe (2013) who documented that hedge

funds that are relatively unconstrained are the only set of traders who provide these linkages in

participation. While member proprietary traders’ income from their brokerage functions may

contain a portion stemming from trading with hedge funds, it is not possible to disentangle who

the outside customers are in our dataset.

Cross market linkages with other commodity markets may also impact member

proprietary trading activities and profitability. In the past, prices of crude oil and natural gas

followed closely with one another and major users viewed the products as close to perfect

substitutes (Onur, 2009). Research has shown that this relationship has diverged (Serletis and

Ricardo, 2004; Baschmeir and Griffin, 2006; and Serletis and Shahmoradi, 2006). In the short

term, prices of oil and natural gas are driven by different fundamental factors with crude oil

prices fluctuating in response to speculative activity in world oil markets and natural gas prices

responding to productive shocks. Azzarello et al. (2014) document a 330% energy content price

gap, which is primarily attributed an increase in production in natural gas. Income stemming

from brokerage functions would be influenced by cross-commodity linkages, not necessarily

income from proprietary trading.

Here we examine the distribution of income for active, proprietary trading in Panel A of

Table 2. Daily average income for options (in dollars) for each proprietary trade across the

nearest three expirations is found by marking to market each trade over the course of a trader

day, summing the income for each individual trader, and averaging the income for each trader

over all trader days by contract expiration. If the trade is a sell, the income is found by taking the

difference between the trade price and the settlement price and multiplying by the quantity. If the

trade is a buy, the income is found by taking the difference between the settlement price and the

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trade price and multiplying by the quantity. The quartiles of daily income are found from the

total daily income levels for each trader. Thus, the minimum corresponds to the lowest level of

income made by an individual trader during the sample period for a specified contract expiration.

Panel B in Table 2 on the other hand details the distribution of average daily proprietary income

across all traders each day. Thus, we have two views of income: among traders and across

traders.

Both tables provide similar results: 25% of traders are unprofitable, while the mean profit

levels, albeit small on average, are positive across traders and days; however Table 2 documents

a slightly skewed distribution with more traders taking a positive profit than a loss on average.

The low levels of profitability beg the question of why member proprietary traders are willing to

provide liquidity to the market, if one average, they are only making low levels of returns. A

negatively skewed return distribution will increase the loss probability, while a positively

skewed return distribution will increase the probability of gaining. A preference for positive

skewness will cause investors to require lower rates of returns on these assets (Barberis and

Huang, 2008; Boyer, Mitton, and Vorkink, 2010), and, as such, a preference for skewness

represents a desire to gamble. Given that option traders often trade based on skew, the relatively

low levels of profit seen on average could be the result of member proprietary traders being

willing to take lower average daily returns for the possibility of big upside potential of these

highly skewed assets.

[Insert Table 2 about here]

C. Market Making Competition

Futures and option markets have systems that can be identified as having market-making

competition, which is in stark contrast to the designated system of the NYSE specialist.

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Competition among dealers has been found to lower spreads (Stoll, 1978; Benston & Hagerman,

1974; Tinic & West, 1972, Wahal, 1997; Klock & McCormick, 1999). Understanding the

dynamics of the price setting and trading behaviors of market makers requires an evaluation of

the competitive forces among this group of traders. The average number of traders is

documented across trade type and contract expiration in Table 3 to determine the extent of

competitive forces in each of the various trade categories. Traders in these markets can conduct

more than one type of trade. The vast majority of traders are classified as making CTI = 1 trades,

which indicates they own 10% or more in the trading account for which they are trading. On

average there are 51 traders executing trades of any type and maturity (first three nearest to

expiration contracts) per day.

[Insert Table 3 about here]

D. Interdealer Trading

In inventory microstructure models market makers face exogenous demands to buy and

sell and profit from buying and selling at bid and ask prices respectively, with the spread

dependent on the underlying risk of the asset. Bid and offer placement are adjusted to manage

inventory risk (e.g. Ho and Stoll, 1983; Manaster and Mann, 1996). Further, as discussed in

Locke and Sarajoti (2004), interdealer trades are typically more costly to initiate than trades

conducted with other trade groups; thus, the only rational explanation for the existence of a

significant percentage of interdealer trades is inventory control. These traders would rather

immediately transfer their unwanted inventory than face the uncertainty of waiting for customer

orders. Table 4 details the percentage of trades by customer type in the options market through a

frequency analysis of trade combinations across the three nearest expiration contracts to examine

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the extent of interdealer trading in the options market. The levels of interdealer trading range

from 16.33% in the second deferred contract to 22.83% in the nearby contract.

[Insert Table 4 about here]

E. Summary of Market Making Activities

The institutional characteristics of futures-options markets indicate that on average,

member proprietary traders in this market trade often, in small amounts, with very little time in

between trades, and are responsible for one of the highest levels of activity in terms of volume.

Thus, these traders serve similar market making roles in both the futures and futures options

markets. Further, it is shown that the levels of competition among these traders are higher than

other trade type categories and member proprietary traders are prone to engaging in interdealer

trading. Competition will lower the average levels of profitability for these traders, as will

engaging in interdealer trades. These two factors may be the driving forces behind the low levels

of profitability within this trade type. However, even given low levels of profitability, market

making in options futures markets is a profitable trading strategy. These summary measures shed

first light on the institution framework under which member proprietary traders make their

market. In order to understand more fully the constraints that these traders face and how these

frictions can help explain the behavior and price setting practices of market makers in futures-

option markets, the risk structure of member proprietary traders follows.

IV. RISK MANAGEMENT

Analysis of market-making risk dynamics in options markets has received very little

attention in the literature and has primarily focused on the overall risk that option market makers

bear. The risk exposure of the option market maker will determine how and whether the market

maker is able to dispel certain portions of risk which will ultimately drive his or her trading and

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price setting behavior. Agarwal and Narayan (2004) characterize risk exposures and portfolio

decisions involving hedge funds, and they find that investors wishing to earn risk premia

associated with different risk factors need to differentiate hedging strategies. Research has shown

that the risk that option market makers are exposed to greatly depends on the stochastic nature of

the underlier’s returns.

Ho and Stoll (1983) showed that, if the stock return volatility is constant, the market

maker’s risk exposure per dollar of investment is nonstochastic over the interval during which

the inventory is held. However, unless the option market maker can trade continuously, an option

transaction’s contribution to the dealer’s risk exposure will be stochastic because the volatility of

an option is a function of both its (stochastic) hedge ratio and the underlying asset’s return

volatility.

Jameson and Wilhelm (1992) evaluated the risks that options market makers face and

provided empirical evidence that their risk factors are unique to option markets due to the

stochastic volatility of the stock return and the inability to rebalance the option position

continuously. Specifically, by measuring the impact of delta, gamma, and vega on bid-ask

spread, they found that gamma and vega are significant determinants of spreads. These risks can

be reduced through diversification; however, the authors’ finding of significant influence of the

risks on spreads indicates that diversification does not completely eliminate the risk due to

discrete rebalancing and stochastic volatility on the option market makers’ portfolio.

O’Hara and Oldfield (1986) utilize a dynamic framework of market makers facing

uncertainty with future order flow and future value of underlying equity, and demonstrated that

inventory and risk preferences have a pervasive influence on the market makers’ pricing policy,

influencing both the size and placement of the spread. These results were further examined by

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Giannetti, Zhong, and Wu (2004) when they developed an inventory-based approach to study

market-making behavior in option markets. They posit that the hedging practices of option

market makers have a substantial impact on the setting of bid-ask spreads and optimal inventory

control. By adding hedging mechanisms to the standard inventory-control model, the authors

derived the market makers optimum option quote setting and inventory-control policies. Huh, et

al. (2012) further develops a theoretical model which evaluates the relationship between hedging

practices of option market makers and the size of the bid ask spread. Here it is posited that the

bid-ask spread increases when option market makers use the underlying market to hedge visa-a-

via using the options market to hedge.

Of vital importance to studying market maker behavior in option markets is evaluation of

these traders’ exposure to and management of risk. Option market makers’ primary exposure to

risk comes from price movement in the option and underlying asset markets, rebalancing needs,

and volatility of the underlying assets. As noted above, much of the previous research in the

literature has focused on the price movement and stochastic nature of the underlying assets.

However, to determine the overall extent of option market makers exposure to risk, inventory

positions must be examined in terms of a vector of risk measures, which include delta, gamma,

and vega. Exposure to these risks is due to the influence of certain variables on the option price.

Several variables are known to affect option prices: the price of the underlying asset, the options

strike price, the time until expiration, the volatility of the price of the underlying asset, the risk

free rate, and the value of the dividends expected during the life of the option.

The primary purpose of this article is to explore the activities and risk management of

market makers in options markets. Here, the sensitivity of the option price to both the price of

the underlying asset and the volatility of the price of the underlying asset are evaluated through

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an examination of delta, gamma, and vega. The underlying volatility not only plays a role in the

valuation of the options being traded, but also in the ability of market makers to eliminate their

exposure to price and volatility risk. The predominant issue is whether market makers in options

futures markets maintain instantaneous delta neutrality as posited in the theoretical literature. If

market makers establish positions in both the underlier and in options that are hedged with

respect to fluctuations in the price of the underlying asset, their portfolios will be delta neutral. It

is found that the member proprietary traders examined in this article do not hedge

instantaneously, which exposes them to fluctuations in the value of their portfolios when the

underlier fluctuates.

Delta measures the degree to which an option price will move given a change in the

underlying asset or, in this case, the sensitivity of the option to the futures price. The delta is

often called the neutral hedge ratio; with a portfolio of n shares of a stock, n divided by delta

gives the number of calls needed to be written to create a neutral hedge. A positive delta

indicates that the option position will rise in value as the stock price rises and drop in value as

the stock price falls. A negative delta, on the other hand, means that the options position should

rise in value if the stock price falls and drop in value if the stock price rises. The delta of a call

option can range from 0 to 1, whereas the delta of a put option can range from -1 to 0. Thus, a

short call has a negative delta, and the long call has a positive delta with these values reversed

for puts and the same for stocks. The closer an option’s delta is to either -1 or +1, the more the

price of the option will respond like an actual long or short stock when the stock price fluctuates.

Gamma indicates how much the delta changes for a $1.00 change in the stock price. It is

the second partial derivative of the option price with respect to the underlier. If gamma is small,

delta changes slowly, and to keep a portfolio of options delta neutral one can rebalance the

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portfolio less frequently. If gamma is large, delta is extremely sensitive to changes in the

underlying price, and, therefore, the portfolio will have to be adjusted more frequently. Both long

calls and puts have positive gamma. That is, long call positions will have deltas that become

more positive and move towards 1 when the underlying price changes but move toward zero

when the underlying price falls. Long puts will have deltas that move toward -1 when the stock

price falls and move toward 0 when the stock price rises. Short calls and puts have negative

gamma; thus, the opposite effects take place. Futures will always have a gamma of zero because

the delta value is always 1.0; thus, it never changes.

The vega of an option indicates how much the price of the option will change as the

volatility of the underlying asset changes. Vega is calculated to show the theoretical price change

for every 1% point change in implied volatility. Long calls and puts both have positive vega,

which indicates that the value of the option will increase as the volatility increases and decrease

when volatility decreases. Short calls and puts both have negative vega, which means that the

value of the option will increase when volatility decreases and decrease when volatility

increases. Vega is the greek which has the most impact on option prices second to delta. Jameson

and Wilhelm (1992) showed that an options gamma and vega were important in the

determination of option market makers’ bid-ask spreads and provided an indication of the

inventory-risk exposure these traders faced.

The risk characteristics of a portfolio of options can be described by the sum of the risk

characteristics of the portfolio components. Central to the evaluation of the risk characteristic

that provides the most information about exposure to inventory-holding risk is whether market

makers in option markets maintain delta neutrality by hedging their trades in the option market

with offsetting positions in the underlying futures market. While many have speculated this to be

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the case, due to data limitations, it has not been formally tested. This unique data set facilitates

the evaluation of traders’ positions in both the futures and option markets, which allows for

incorporation of information about whether these traders are maintaining delta neutral positions

by conducting simultaneous, off-setting trades. Two issues are addressed in the analysis that

follows: (1) Do option market makers use the underlying futures market to maintain delta

neutrality? and (2) How are market makers managing their exposure to sources of rebalancing

and volatility risk? These questions are addressed by evaluating the market maker’s risk

holdings at varying intervals intraday.

A. Position Risk Parameters

If a trader simultaneously trades in both the option and futures markets, position delta

will reflect the extent to which the trader is maintaining a delta-neutral portfolio at the end of

each day by creating offsetting trades from participation in both markets. If the trader is only

participating in the option market, the position delta is calculated using only the trades from the

option market and will also provide information about end-of-day delta neutrality. The gamma

and vega of futures are zero; thus, those values incorporate only information about trades in the

option market.

In order to facilitate the analysis of the position parameter levels, several simplifying

assumptions must be made. First, it is assumed that traders conducting member proprietary

trades begin each trading day with an inventory level of zero. Manaster and Mann (1996)

provided evidence that daily changes in inventory are concentrated around zero, so we follow the

previous literature which assumes that all traders begin the day with a zero-inventory position.

Second, while the analysis for the option market is performed by broker identification numbers,

which are unique for a particular trader, in order to track trades from the option to the futures

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market, account numbers must be used when matching trades in both markets2. The trades are

matched by account number and time; thus, it is assumed that if a trade occurs within a specified

time frame for the same account, it is instigated by the same broker. There may be more than one

broker per account number; therefore, noise will be introduced into the matching process.

Finally, trades in the options market will contain only those performed by traders conducting

CTI 1 trades, whereas they are matched with both CTI 1 and CTI 3 trades from the futures

market because a trader in either category of trade in the futures market could in practice be

executing offsetting trades for the option market makers.

In order to calculate the parameter estimates, a price series must be formed for the option

and futures markets. There are two issues to address in forming a matched price series for the

option and futures markets: (a) which contract expiration to use and (b) how to address

nonsynchronous trading issues. The first issue arises because the contract with the highest

volume may not be the nearby contract. Volume is well known to be a proxy for information and

is highly related to open interest; thus, we use both the nearby and first deferred contracts which

contain the highest overall levels of volume for this analysis. The second issue arises because

futures markets are much more active than the relatively illiquid option market; thus, issues

involving nonsynchronous trading must be addressed. NYMEX requires that trades be reported

within one minute of execution, so we aggregate prices over a one-minute time span in order to

form a price series that reflects the volume weighted average price for a minute for both the

futures and options markets.

2 A subsample was also studied that evaluated the position risk positions matched by executing broker IDs after

electronic trading in futures markets began because in theory option market makers could simultaneously trade in

both markets using hand held devices. Our findings were insignificantly different and robust to the matching

procedure using account numbers.

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Volume-weighted average prices for observations from proprietary trades (CTI 1 trades)

for the nearby and first deferred contracts are computed over one minute interval for both the

option and the futures markets. The volume weighted average prices are found by multiplying

the trade price for a given observation by the quantity traded at that price with the average taken

over all observations in a minute. The last observation at each strike, for each option type (put

and call) is taken along with the futures-settlement price in an increment, where the last volume-

weighted average futures price in the increment is used as a proxy for the settlement price.

These values are used in a binomial pricing model to estimate the option premiums.

The binomial option-pricing models the underlying instrument over time, as opposed to a

particular point in time; thus, it is used to allow for the early exercise component of futures

contracts. Also known as American-style options, which can be exercised at any point in time,

early exercise is a unique feature of options on futures contracts that stems from the minimal

time value associated with in-the-money futures options. It is advantageous to exercise in-the-

money futures options early and reinvest the proceeds at the risk free rate in order to earn a

higher overall rate of return, which unique to these types of options.

An implied standard deviation is used as a proxy for F which, along with the time

duration of a step t, measured in years, is used to calculate the probability that the price of the

underlying asset will move up or down at each step in the binomial tree. This implied standard

deviation is calculated from the most actively traded, near-the-money option for the settlement

futures price3. A grid search is used to find the implied standard deviation, which minimizes the

mean-squared error over the trading day by comparing the average option premium to the

observed premium for each hypothetical sigma.

3 Bloomberg implied volatilities were also used with no significant changes in the results. Thus, our estimation of

the implied volatility is robust to the methodology described.

19

This method ensures that the tree is recombinant, which reduces the number of tree nodes

and speeds up the computation of the option price. This property also allows for the underlying

price to be calculated directly from a formula at each node rather than from having to build the

entire tree. It is well known that option valuations cycle from high to low as the number of steps

increases, holding time to maturity constant; therefore, two separate steps are used, 30 and 31, to

calculate the average option value for each hypothetical sigma.

Once the premiums, futures prices, and implied standard deviation have been found, the

delta, gamma, and vega are calculated as in Hull (2000). An estimate of delta, gamma, and vega

are computed for each strike price and option type (put and call) in each increment. The

estimated risk parameters are merged back with the trader level data to compute position

parameter values for each trade. This is done by summing the quantity of trade for a particular

strike and option type for each trader in an increment, which is then multiplied by the

corresponding (option type and strike) estimated parameter values to compute the position

parameter value for each trader in each increment. The position levels are marked to market at

the end of each increment to account for open positions (either long or short) in the computation

of the position parameter levels.4 These position parameter values are examined in greater detail

to examine option market makers exposure to various sources of intraday risk in the sections that

follow.

B. Delta Neutrality

The theoretical literature on option risk management postulates that option market

makers may hedge inventory risk exposures by maintaining delta-neutral positions (Figlewski,

4 Marking the position parameter levels to market each increment entails summing the positions of each increment to

carry forward the balance (if the trader is net long in the increment) or debit (if the trader is net short in the

increment) of trades. The balance is then added to the first trade in the increment and multiplied by the increment’s

parameter estimate to calculate the increment’s parameter position level.

20

1989; Cox & Rubinstein, 1985). This would require option market makers to engage in hedging

by (for example) purchasing a quantity of futures options while simultaneously executing a

certain number of contracts in the underlying futures contract, seeking instantaneous delta

neutrality. The degree to which these traders hedge by participating in both markets will

determine their vulnerability to the risk of holding positions in the option market. The short-run

exposure of the futures-option market maker to price risk, delta, is expected to be small if they

are instantaneously delta-hedged while the exposure to volatility, vega, may more accurately

represent the “inventory” that the market maker is carrying.

As specified above, the futures and options data are matched by account numbers and

time to determine whether (1) instantaneous hedging is taking place and (2) if instantaneous

hedging is not being used, examining the process by which option market makers use futures

markets to hedge during the course of a trading day. Table 5 reports the results that depict

whether option market makers are instantaneously delta neutral by matching the options and

futures data by account number and time; where we make the assumption that if a trade takes

place under the same account number in the same minute the futures trade corresponds to the

options trade that was executed in that same time frame. We find that contrary to theory, option

market makers do not maintain instantaneous delta neutrality.

[Insert Table 5 about here]

Due to this finding, an additional analysis is performed to determine whether option

market makers tend to specialize in hedging in a particular market. To evaluate whether option

market makers specialize in hedging only in options or in futures the first month of the sample,

September 2005, is evaluated. A frequency analysis of the number of traders engaging trades in

both the futures and option markets versus the option market only is performed. The frequency

21

provides a count of the number of trades for a particular trader. Of the 65 option market makers

who were trading in September 2005, 25, or 38.64%, traded only in the option market and did

not use the futures market to hedge. Of these traders, their overall trading activity is very low,

capturing only 3.8% of the overall number of trades conducted that month. Forty, or 61.54%, of

the options market makers engage in trading in both markets. The number of trades in the futures

market far surpasses the number of trades in the options market with 3020 and 4452 trades in

options and futures respectively.

Thus, hedging options trades in the futures market is not a one-for-one strategy. Trading

in options captures 38.88% of the overall number of trades for the month, whereas trades in the

futures market are at about 57.32%. Higher amounts of trading in the futures market may be one

explanation for why the levels of position delta are higher when both option and futures trades

are evaluated than when only the options trades are evaluated. Market makers who are using both

markets to hedge may be overestimating their exposure to price risk, resulting in holding (or

selling) too many of the underlying futures contracts to offset their positions in the options

market.

There are other explanations as well however: first, option market makers trade

frequently and in small amounts as is documented in Table 1; therefore, many of their option

trades are liquidated quickly which would eliminate the need for hedging in the futures market.

Further, if they are unable to unwind these positions efficiently and quickly, it may be an impetus

to eventually go into the futures market to offset their inventory holding risk exposure. The

desire to keep bid-ask spreads to a minimum as postulated in Huh et. al. (2012) in order to keep

liquidity high may also be a reason for the above findings.

22

The ability of market makers to liquidate their inventory holdings quickly and efficiently

using futures markets is examined by widening the interval by which options are matched with

the futures trades to better capture the hedging activity being employed by the option market

makers. Two primary filters are used: (1) 600 seconds and (2) the trading increment which

consists of one hour of trading, except the initial increment that consists of the first 2 hours of

trading.5 The results from this analysis are presented in Table 6, with Panel A presenting the

merge base of 600 seconds and Panel B containing the results from the increment merge base.

From this analysis it appears that market makers actively seek to utilize the underlying futures

market to hedge their nearby contracts more than the further to expiration contracts. Further

when comparing the alternative merge base specifications of 600 seconds and an increment with

the instantaneous hedging (within one minute), it appears that lengthening the time frame

captures greater amounts of market maker hedging activities. This analysis supports the notion

that while market makers in options markets do not maintain instantaneous delta neutrality, they

do utilize the underlying futures market to hedge inventory that either was not easily liquidated

quickly or is being held onto for a period of time to possibly allow for prices to adjust to some

acceptable level.

[Insert Table 6 about here]

We also examine whether there are differences between large and small traders in their

risk management. We split the sample into two categories of traders: large traders, or those who

maintain an absolute value of quantity traded during an increment of 30 contracts or more and

small traders, or those who fall below 30 contracts in any given increment. The results of this

analysis are presented in Table 7, which indicates that large traders are the primary users of the

futures market for hedging purposes. Small traders do not maintain delta neutrality as shown by

5 Due to the lack of trading in the first hour, the first 2 hours of trade are combined for the incremental analysis.

23

the larger levels of position risk when including the futures trades than when not. It may be that

larger traders are more adept at managing their inventory holding risk due to their frequent needs

to dispel this risk because of their much larger holdings on average. The levels for the position

risk holdings are significantly lower when including the futures trades corresponding to the

options transactions made within the same increment across both maturity spectrums (nearby and

first deferred). Small traders on the other hand are primarily trading frequent, small amounts in

the options market with limited trading taking place in the futures market, thus eliminating the

need for futures market hedging.

[Insert Table 7 about here]

C. Intraday Analysis of Gamma and Vega

Of further importance is whether and how the market maker’s other position risks are

changing over the course of the trading day. Examining the intraday values of gamma and vega

allows for a decomposition of the characteristics that option market makers manage in order to

mitigate their exposure to various sources of risk. By evaluating the distribution of the risk

characteristics over the trading day, it can be determined whether any intraday patterns in risk

management exist for market makers in the options market.

Intraday market-maker gamma and vega risk is evaluated over five time increments in

Table 8. Panel A denotes the position risk parameters averaged over all traders. Both gamma

and vega exhibit a u-shaped pattern across the increments indicating increased levels of risk on

average at the beginning and end of the trading day when volume is also the highest. Significant

differences for position gamma correspond to the higher volumes at the beginning and end of the

trading day, while position vega has a significant drop at midday when volumes are typically at

24

their lowest levels. Thus, on average the risk management practices of market makers seem to

follow typical trends in volume.

[Insert Table 8 about here]

Panel B (C) of Table 8 provides the position gamma and vega by increment for large

(small) traders. For large traders both gamma and vega experience relatively flat levels over the

course of the trading day with a significant increase in the last increment. Interesting differences

can be noted between the contract expirations where the first deferred levels of position vega are

of three orders of magnitude larger than the nearby contract. It appears that large option market

makers focus their volatility risk management on the nearby contract. For small traders, position

gamma decreases with contract expiration while position vega is two orders of magnitude larger

in the first deferred contract.

D. The Microstructure of Risk Management

In Table 9 we partition the increment position risk parameters based on number of trades,

trade size, and volume to determine whether any of these market microstructure characteristics

play a role in the management of intraday risk by option market makers. Across all of the sample

partitions we see a very large amount of dispersion among the quartiles especially between the

lower 50% and upper 50%, which again suggests that significant differences in trading and risk

characteristics are present among large versus small traders. Those with the highest levels of

trading activity, with the largest trades, and those who generate the highest amounts of volume,

all exhibit the greatest amounts of risk management: delta risk appears to exhibit an inverted U-

shape across the trading increments; vega risk is highest in the first two increments and virtually

flat across the latter three time increments; gamma risk seems to fluctuate within some

25

acceptable range. No discernible pattern exists for the lowest quintile for vega risk, but delta risk

for this group also exhibits an inverted u-shape across the trading day.

[Insert Table 9 about here]

E. Does Moneyness Matter?

Due to the various costs in trading different types of options market makers may tend to

trade in particular categories of moneyness. This issue is evaluated with the results presented in

Table 10. It is reasonable to assume that certain traders may choose to specialize in a group of

options determined by moneyness due to the relative differences in cost and structure of the

various option types. For instance, deep in-the-money options are almost perfect substitutes for

the underlying security, while in-the-money options are the cheapest. If option market makers

have certain trading strategies based on the differences between moneyness categories, patterns

in trading certain options should emerge.

[Insert Table 10 about here]

A moneyness level of 3% is chosen because it offers the greatest range of observations in

each moneyness group. A frequency analysis is performed to determine whether market makers

specialize in moneyness groups. This analysis reveals that the vast majority of options market

makers trade in all types of moneyness with only 11 of the 65 trading in only one or two

categories of option moneyness. For those 11 traders, all but two conduct only one trade during

the sample period. Of the remaining 54 traders who participate in trading across all levels of

moneyness, 66.17% of their trades are in out-of-the-money options, 18.87% are in at-the-money

options, and 14.12% of their trades are in in-the-money options as shown in Table 10. Thus, it

does not appear that market makers focus on only one category of moneyness, but instead trade

26

across moneyness groups, with the majority of their trading focused on out-of-the-money

options, probably due to their cost-relative to at-the-money or in-the-money options.

F. Risk and Return

Previous research has documented the impact of the position greeks on bid-ask spread but

since we are interested here in market making as a trading strategy, we evaluate the impact of

each of the position risk parameters on profit. If the risk/return model holds true we expect to

see significant levels of risk being related to profit. The univariate analysis above indicates that

option market makers actively seek to manage their exposure to delta risk over both the nearby

and first deferred contracts, albeit not instantaneously, focus their vega hedging on primarily the

nearby contract, and are subject to significant levels of gamma risk. A simple regression of daily

profit for each trader on the position risk parameters (Delta, Vega, and Gamma respectively)

yielded the following results for the nearby contract where Position Gamma was the only risk

parameter found to have a significant effect on market maker profit:

𝑃𝑖,𝑡 = 4.31 − 14.05𝛿𝑖,𝑡 − 6.14𝜗𝑖,𝑡 + 𝟖𝟏. 𝟕𝟑𝛾𝑖,𝑡 + 휀𝑖,𝑡

These results are in line with those of Jameson and Wilhelm (1992) who found Gamma to have a

positive and significant effect on the spread and also correspond to the theoretical design

constructed in Huh et. al. (2012) with respect to the ability of a market maker to rebalance

increasing the costs associated with trading.

V. CONCLUSION

The institutional characteristics of traders behind four different trade classifications are

evaluated for the futures option NYMEX natural-gas market in order to decompose trade-type

characterization. It is found that traders conducting member proprietary trading in the natural-gas

27

option market behave as though they are market makers, on average, trading often in small

amounts with very little time in between trades, and are responsible for the highest levels of

activity in terms of volume. They also end the trading day with very low levels of inventory in

order to mitigate their exposure to overnight inventory-holding risk. Evaluation of the extent of

competitive forces in each trade category and the use of interdealer trades to expel unwanted

inventory are also conducted in order to provide more information on the institutional details of

option market making. It is shown that traders who conduct member proprietary trading are one

of the largest trader groups and engage in significant amounts of interdealer trading in order to

maintain their preferred inventory levels.

The portfolios of option market makers are examined in terms of their exposure to daily

levels of risk as measured by delta, gamma, and vega. It is found that end-of day positions are

very small, a result that supports the hypothesis that market makers try to mitigate their exposure

to overnight risk. Intraday, position delta and vega are found to be relatively constant. Position

vega has a significant drop at midday (increment 3) but has insignificant changes and small

levels throughout most of the trading day. Gamma has significant changes between increments 1

and 2 and then again at the end of the trading day between increment’s 4 and 5, which likely

results from higher volumes at the beginning and end of the trading day. These results lend

support to the hypothesis that market makers in options markets work to maintain their exposure

to both price and volatility risk, and are primarily exposed to the effects of rebalancing risk.

Analysis of the relationship between the position risk parameters and profits shows a significant

and positive relationship between profitability and position gamma risk exposure.

When comparisons are made between large and small traders it is found that large traders

utilize the underlying futures market to hedge price risk, but only at longer time horizons. One

28

explanation for this is that the underlying futures market is used by option market makers

wanting to dispel their inventory holding risk that cannot be eliminated in the option market;

indicating a preference for managing risk using options. The exposure of large traders to

rebalancing and volatility risk is significantly higher than that of smaller traders, as larger traders

inventories are more cumbersome to manage throughout the trading day.

This article provides an in-depth, descriptive analysis of how market makers in option

markets make their market and lays the foundation for a wealth of future research paths. Future

research directly stemming from this analysis should evaluate how changes in risk holdings

affect the prices that market makers maintain. Patterns in bid-ask spreads are well documented;

thus, the intraday changes in risk holdings and the movement of traders into and out of the

market may serve as additional measures to help explain their U-shaped patterns. Other issues

that deserve further examination include how option market makers are using the option market

to mitigate their exposure to price risk, the impact of a market event on the number and ability of

traders providing market-making services, as well as the extent to which interdealer trading

impacts risk levels and, ultimately, market prices. These are largely unaddressed areas in the

literature and warrant further investigation. This paper serves as the basis for a fruitful stream of

future research surrounding market making in option markets.

29

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Table 1: Summary Statistics for NYMEX Natural-Gas Options Trading

Table 1 displays summary statistics for the most active traders for all trade categories over the first three nearest contract months for

options. The level of analysis used to conduct the testing of whether member proprietary trader behavior is indicative of that of market

makers in futures options is meant to provide an indication of how an average trader conducting a certain type of trade behaves and

the characteristics of each type of trade. The total number of trades each day is determined through a frequency analysis that provides

a count of the number of trades every day by each trade group across the three nearest contract expirations. The daily average number

of trades is found by taking the average of the total number of daily trades obtained from the frequency analysis (the total number of

trades divided by the number of trader days). The daily average volume is found by first summing the total quantity of purchases

traded in a day (buy observations only) by an individual trader for a trade type and contract expiration. This provides the total sum of

quantity traded for each trader on every day for a trade type and contract expiration. This total is averaged over the total trader days by

trade category and contract expiration to obtain a daily average level of trading volume. The average trade size is found by evaluating

the average quantity traded for each trade category and expiration. The average time between trades is found by evaluating the average

time between each trade for each trade category and expiration.

Summary Statistics for NYMEX Natural-Gas Options

CTI

Daily average

number of trades

Total number

of trades

Daily average

volume

Total

volume

Average

trade size

Average time

between trades

Nearby contract

1 89 36,646 167 2,154,761 29.43 18.42

2 5 1,511 263 226,920 66.13 15.06

3 4 1,499 145 176,675 55.23 15.07

4 55 22,617 259 1,928,015 43.39 15.06

First deferred contract

1 47 19,179 121 1,232,891 32.13 15.93

2 4 864 324 189,577 95.27 12.42

3 2 501 133 63,144 60.52 17.31

4 33 33 225 1,281,987 48.52 15.92

Second deferred contract

1 26 10,789 99 691,003 31.23 12.76

2 3 470 272 99,440 95.26 14.74

3 2 266 154 43,036 80.16 15.37

4 20 8,010 193 837,020 53.95 14.01

33

Table 2: Distribution of Proprietary Trader Income

Panel A in Table 2 displays the distribution of income for active, proprietary trading. Daily average income for options (in dollars) for each proprietary trades

across the nearest three expirations is found by marking to market each trade over the course of a trader day, summing the income for each individual trader, and

averaging the income for each trader over all trader days by contract expiration. If the trade is a sell, the income is found by taking the difference between the

trade price and the settlement price and multiplying by the quantity. If the trade is a buy, the income is found by taking the difference between the settlement

price and the trade price and multiplying by the quantity. The quartiles of daily income are found from the total daily income levels for each trader. Thus, the

minimum corresponds to the lowest level of income made by an individual trader during the sample period for contract expiration. Panel B in Table 2 displays

the distribution of daily income where each day a proprietary trader’s income is calculated by marking to market all of their trades at daily settlement prices. An

average across all traders is taken to obtain a daily average income for each day in the sample. This table represents the distribution of the daily average incomes

across 413 days with the top row containing all trades and the next three incomes broken out by expiration.

Panel A: Income Distribution

Contract N Mean Minimum 25% Median 75% Maximum

All trades 15,573 $228 -$1,799,279 -$162 $60 $500 $1,779,416

Nearby 13,503 $245 -$422,450 -$375 $50 $800 $445,018

First Deferred 10,944 $267 -$5,396,627 -$150 $25 $470 $5,333,350

Second Deferred 7,760 $331 -$122,190 -$40 $0 $250 $697,990

Panel B: Daily Income Distribution

Contract N Mean Minimum 25% Median 75% Maximum

All trades 413 $224 -$8,842 -$175 $145 $585 $10,820

Nearby 413 $229 -$20,966 -$350 $188 $970 $12,717

First Deferred 413 $254 -$6,864 -$289 $113 $732 $16,068

Second Deferred 413 $331 -$12,777 -$195 $49 $444 $53,248

34

Table 3: Number of Traders

The table presents the daily average number of traders executing the various types of trades in options market across

our sample. A trader trades a CTI=1 trade when they own 10% or more in the trading account for which they are

trading. CTI=2 executed trades are for the traders clearing member account. CTI=3 trades are executing for other

floor traders who are present on the floor. A trader executes a CTI=4 trade when the principal behind the trade is a

non-member, or a customer. Traders may execute all 4 of the trade types for all contract maturities. There are on

average 51 traders executing trades of any type and any maturity per day.

CTI Average number of traders

Nearby contract

1 31

2 2

3 3

4 18

First deferred contract

1 25

2 2

3 2

4 14

Second deferred contract

1 17

2 1

3 1

4 10

35

Table 4: Interdealer Trading Options

The percentage of trades by customer type in the options market is determined through a frequency analysis of trade

combinations across the nearest three expiration contracts to examine the extent of interdealer trading in the options

market. Interdealer trades are identified when both the initiator of the trade and the opposite trader are both trading

for their personal accounts.

Trader Opposite trader Percentage of trades by customer type

Nearby Contract

Personal Personal 22.83%

Personal House 3.30%

Personal Other floor 3.96%

Personal Customer 64.79%

House House 0.05%

House Other floor 0.17%

House Customer 1.29%

Other floor Other floor 0.03%

Other floor Customer 0.61%

Customer Customer 2.97%

First Deferred Contract

Personal Personal 17.82%

Personal House 3.42%

Personal Other floor 2.29%

Personal Customer 71.30%

House House 0.07%

House Other floor 0.09%

House Customer 1.41%

Other floor Other floor 0.02%

Other floor Customer 0.53%

Customer Customer 3.05%

Second Deferred Contract

Personal Personal 16.33%

Personal House 2.98%

Personal Other floor 1.99%

Personal Customer 72.82%

House House 0.07%

House Other floor 0.10%

House Customer 1.58%

Other floor Other floor 0.02%

Other floor Customer 0.60%

Customer Customer 3.51%

36

Table 5: Delta Risk Analysis Merge Base of 60 Seconds Table 5 provides evidence testing the hypothesis that option market makers maintain instantaneous delta neutral

positions. The trading day is partitioned into five increments. Using the last trade for both options and futures in a

time increment, an implied standard deviation is found for each time increment, which minimizes the sum of

squared errors between the options price estimated by the binomial option pricing model and the observed options

incremental settlement price. This implied standard deviation is then used to compute the delta for all option strikes

and types (puts and calls) in each increment. For each trader, the quantity of trade is summed over the increment and

multiplied by the estimated parameter values to compute the trader’s exposure to portfolio risk as measured by

position delta. The variable options and futures delta include futures trades placed within 60 seconds of the options

trade under the same account number. The absolute value of each trader’s position risk parameter for each trade is

taken and averaged over all traders trading in a given increment. The positions are marked to market each increment

by summing the quantity traded over a particular increment for a trader and using that level as the beginning

inventory level for the next increment.

Delta Risk Analysis: Merge Base of 60 Seconds

Nearby Contract

Increment

Options

Delta Options and Futures Delta Difference

t-

Value DF

p-

Value

1 13.80 15.57 -1.77 -6.69 9224 <.0001

2 18.31 19.99 -1.68 -5.67 11257 <.0001

3 21.83 23.81 -1.98 -5.73 12200 <.0001

4 23.72 26.21 -2.49 -6.72 12892 <.0001

5 26.11 29.32 -3.21 -7.81 13265 <.0001

First Deferred Contract

Increment

Options

Delta Options and Futures Delta Difference

t-

Value DF

p-

Value

1 7.67 9.11 -1.43 -5.92 6598 <.0001

2 10.49 12.02 -1.53 -4.77 8595 <.0001

3 13.04 14.44 -1.40 -4.1 9584 <.0001

4 14.53 16.04 -1.52 -3.93 10333 <.0001

5 16.04 18.23 -2.19 -4.96 10787 <.0001

37

Table 6: Delta Risk Analysis with Alternative Merge Base Specifications Table 6 explores alternate matching specifications of futures and options trades to explore option market markets

position delta risk management strategies. The trading day is partitioned into five increments. Using the last trade

for both options and futures in a time increment, an implied standard deviation is found for each time increment,

which minimizes the sum of squared errors between the options price estimated by the binomial option pricing

model and the observed options incremental settlement price. This implied standard deviation is then used to

compute the delta for all option strikes and types (puts and calls) in each increment. For each trader, the quantity of

trade is summed over the increment and multiplied by the estimated parameter values to compute the trader’s

exposure to portfolio risk as measured by position delta. The variable options and futures delta include futures

trades placed within either (1) 600 seconds (Panel A) or (2) increment (Panel B) of the executed options trade under

the same account number. The absolute value of each trader’s position risk parameter for each trade is taken and

averaged over all traders trading in a given increment. The positions are marked to market each increment by

summing the quantity traded over a particular increment for a trader and using that level as the beginning inventory

level for the next increment.

Panel A: Delta Risk Analysis: Merge Base of 600 Seconds

Nearby Contract

Increment Options Delta Options and Futures Delta Difference t-

Value DF

p-

Value

1 19.68 15.41 4.28 6.1 3738 <.0001

2 18.75 13.10 5.65 7.57 3069 <.0001

3 20.15 14.84 5.32 6.12 2545 <.0001

4 17.60 14.29 3.31 4.27 2435 <.0001

5 16.43 18.75 -2.32 -2.73 2216 0.0063

First Deferred Contract

Increment Options Delta Options and Futures Delta Difference t-

Value DF

p-

Value

1 11.99 13.48 -1.49 -2.42 2054 0.0157

2 13.54 14.59 -1.06 -1.22 1558 0.2232

3 13.32 14.72 -1.4 -1.62 1175 0.1061

4 13.70 15.71 -2.01 -2.31 1129 0.0208

5 17.16 20.63 -3.46 -2.02 1069 0.0435

Panel B: Delta Risk Analysis: Merge Base of Increment

Nearby Contract

Increment Options Delta Options and Futures Delta Difference t-

Value DF

p-

Value

1 20.61 19.49 1.12 1.72 4517 0.0859

2 19.38 16.92 2.46 3.69 3732 0.0002

3 20.74 18.47 2.28 2.92 3125 0.0035

4 18.16 17.98 0.18 0.24 2981 0.8083

5 17 21.22 -4.22 -4.92 2548 <.0001

38

First Deferred Contract

Increment Options Delta Options and Futures Delta Difference t-

Value DF

p-

Value

1 12.1 16.19 -4.09 -6.99 2658 <.0001

2 13.17 16.45 -3.28 -4.28 2036 <.0001

3 13.08 16.21 -3.12 -3.95 1570 <.0001

4 14.18 18.35 -4.17 -5.41 1499 <.0001

39

Table 7: Delta Risk Analysis By Trader Size with a Merge Base of Increment Table 7 explores differences between large and small traders with regards to the management of their position delta

risk. A large trader is defined as one whose absolute value of quantity of trade in a given increment is 30 contracts

or more, while a small trader is one who trades below this same threshold. The trading day is partitioned into five

increments. Using the last trade for both options and futures in a time increment, an implied standard deviation is

found for each time increment, which minimizes the sum of squared errors between the options price estimated by

the binomial option pricing model and the observed options incremental settlement price. This implied standard

deviation is then used to compute the delta for all option strikes and types (puts and calls) in each increment. For

each trader, the quantity of trade is summed over the increment and multiplied by the estimated parameter values to

compute the trader’s exposure to portfolio risk as measured by position delta. The variable options and futures delta

include futures trades placed within an increment of the executed options trade under the same account number. The

absolute value of each trader’s position risk parameter for each trade is taken and averaged over all traders trading in

a given increment. The positions are marked to market each increment by summing the quantity traded over a

particular increment for a trader and using that level as the beginning inventory level for the next increment.

Panel A: Large Traders with Merge Base of Increment

Nearby Contract

Increment Options Delta Options and Futures Delta Difference t-

Value DF

p-

Value

1 84.13 54.84 29.28 9.46 782 <.0001

2 83.53 48.79 34.74 10.29 600 <.0001

3 91.93 55.92 36.01 10.48 510 <.0001

4 82.42 53.7 28.71 7.26 457 <.0001

5 89.61 68.87 20.73 4.68 336 <.0001

First Deferred Contract

Increment Options Delta Options and Futures Delta Difference t-

Value DF

p-

Value

1 71.48 58.57 12.91 3.07 256 0.0024

2 85.87 61.59 24.28 3.94 187 0.0001

3 78.26 56.82 21.44 3.85 155 0.0002

4 81.2 62.87 18.33 4.24 171 <.0001

5 100.97 68.89 32.08 3.86 146 0.0002

Panel B: Small Traders with Merge Base of Increment

Nearby Contract

Increment Options Delta Options and Futures Delta Difference t-

Value DF

p-

Value

1 7.29 12.08 -4.79 -12.7 3734 <.0001

2 7.07 10.8 -3.74 -10.19 3131 <.0001

3 6.83 11.15 -4.31 -7.65 2614 <.0001

4 6.5 11.5 -4.99 -10.63 2523 <.0001

5 5.94 13.96 -8.02 -11.67 2211 <.0001

40

First Deferred Contract

Increment Options Delta Options and Futures Delta Difference t-

Value DF

p-

Value

1 5.74 11.65 -5.91 -13.09 2401 <.0001

2 5.78 11.86 -6.08 -11.59 1848 <.0001

3 5.9 11.73 -5.83 -9.96 1414 <.0001

4 5.5 12.58 -7.09 -11.3 1327 <.0001

5 5.59 14.64 -9.04 -7.74 1161 <.0001

41

Table 8: Intraday Gamma and Vega Risk Position Levels by Increment

Table 8 evaluates the option market maker’s intraday exposure to Position Gamma and Position Vega, or

rebalancing and volatility risk respectively. The trading day is partitioned into five increments. Using the last trade

for both options and futures in a time increment, an implied standard deviation is found for each time increment,

which minimizes the sum of squared errors between the options price estimated by the binomial option pricing

model and the observed options incremental settlement price. This implied standard deviation is then used to

compute the gamma and vega for all option strikes and types (puts and calls) in each increment. For each trader, the

quantity of trade is summed over the increment and multiplied by the estimated parameter values to compute the

trader’s exposure to portfolio risk as measured by position gamma and vega. The absolute value of each trader’s

position risk parameter for each trade is taken and averaged over all traders trading in a given increment. The

positions are marked to market each increment by summing the quantity traded over a particular increment for a

trader and using that level as the beginning inventory level for the next increment. Bolded values indicate a

significant difference from the previous increment’s value.

Panel A: All Position Gamma and Vega

Nearby Contract

Increment Gamma Vega

1 54.95 14.17

2 51.78 14.73

3 45.57 12.99

4 45.86 13.49

5 64.40 15.02

First Deferred Contract

Increment Gamma Vega

1 33.03 27.00

2 27.29 25.82

3 27.20 25.87

4 29.36 26.72

5 36.60 31.30

Panel B: Large Traders Position Vega and Gamma

Nearby Contract

Increment Gamma Vega

1 157.35 37.53

2 150.82 41.90

3 126.75 39.77

4 130.96 42.64

5 242.15 54.60

First Deferred Contract

Increment Gamma Vega

1 155.33 114.53

2 121.01 124.70

3 103.55 112.92

4 116.89 105.74

5 161.43 139.49

42

Panel C: Small Traders Position Vega and Gamma

Nearby Contract

Increment Gamma Vega

1 34.27 9.46

2 32.12 9.34

3 29.51 7.70

4 30.58 8.25

5 37.52 9.03

First Deferred Contract

Increment Gamma Vega

1 20.08 17.73

2 17.61 15.61

3 18.64 16.11

4 17.93 16.40

5 20.10 17.01

43

Table 9: Subsample Analysis of the Intraday Risk Parameter Position Levels Over Five Time Increments

Table 9 evaluates whether the option market maker’s intraday exposure to their portfolio of position risk holdings is influenced by their number of trades (Panel

A), trade size, or volume traded. The trading day is partitioned into five increments. Using the last trade for both options and futures in a time increment, an

implied standard deviation is found for each time increment, which minimizes the sum of squared errors between the options price estimated by the binomial

option pricing model and the observed options incremental settlement price. This implied standard deviation is then used to compute the delta, gamma, and vega

for all option strikes and types (puts and calls) in each increment. For each trader, the quantity of trade is summed over the increment and multiplied by the

estimated parameter values to compute the trader’s exposure to portfolio risk. The absolute value of each trader’s position risk parameter for each trade is taken

and averaged over all traders trading in a given increment. The positions are marked to market each increment by summing the quantity traded over a particular

increment for a trader and using that level as the beginning inventory level for the next increment.

Panel A: Quartiles Based on the Number of Trades

Variable Increment 1 Increment 2 Increment 3

1 2 3 4 1 2 3 4 1 2 3 4

Position Delta 2.22 2.84 17.38 19.94 5.28 3.58 25.30 33.29 4.23 4.58 28.48 34.86

Position Delta without Futures 2.19 2.92 15.40 18.18 5.10 3.42 19.16 23.83 4.26 3.85 20.85 23.91

Position Gamma 2.16 2.79 30.58 36.16 10.30 5.89 39.20 52.04 7.64 4.55 37.65 41.95

Position Vega 1.28 2.17 13.04 16.25 4.27 3.47 19.08 24.91 3.80 3.84 18.27 24.80

Increment 4 Increment 5

1 2 3 4 1 2 3 4

Position Delta 4.46 4.38 25.77 30.13 2.31 4.98 34.68 28.19

Position Delta without Futures 4.72 3.59 19.28 19.39 2.41 4.45 25.48 20.41

Position Gamma 9.12 6.13 44.80 49.12 4.53 9.51 48.49 53.27

Position Vega 5.62 2.91 18.75 21.04 2.60 3.71 16.64 23.89

Panel B: Quartiles Based on Trade Size

Variable Increment 1 Increment 2 Increment 3

1 2 3 4 1 2 3 4 1 2 3 4

Position Delta 2.91 5.15 13.28 30.82 3.82 7.55 20.98 51.26 4.26 7.60 21.87 53.35

Position Delta without Futures 2.83 4.87 12.56 27.72 3.33 6.38 15.49 36.44 3.73 5.53 14.93 37.46

Position Gamma 4.29 4.58 22.55 58.43 7.97 9.12 32.01 79.84 6.21 7.62 23.26 69.88

Position Vega 2.47 2.97 10.72 24.96 3.42 6.28 15.47 37.53 3.47 5.15 13.57 37.67

Increment 4 Increment 5

44

1 2 3 4 1 2 3 4

Position Delta 4.22 6.83 18.27 45.21 3.03 6.75 17.09 47.25

Position Delta without Futures 3.72 4.96 11.72 29.87 2.68 5.08 12.51 34.86

Position Gamma 6.86 9.48 29.58 76.52 7.18 11.23 29.58 83.90

Position Vega 3.84 4.59 11.61 31.36 3.00 4.18 12.66 34.08

Panel C: Quartiles Based on Volume

Variable Increment 1 Increment 2 Increment 3

1 2 3 4 1 2 3 4 1 2 3 4

Position Delta 1.30 3.47 7.74 27.70 1.60 4.80 11.39 46.69 2.23 6.23 11.01 48.86

Position Delta without Futures 1.35 3.48 7.43 25.30 1.71 4.45 9.70 32.86 1.91 5.06 8.41 33.37

Position Gamma 1.73 3.22 12.83 51.76 3.39 7.51 19.58 70.19 3.77 6.18 14.33 59.67

Position Vega 1.50 2.13 5.92 23.78 2.07 4.14 9.15 35.89 2.72 4.48 7.26 32.98

Increment 4 Increment 5

1 2 3 4 1 2 3 4

Position Delta 3.43 5.23 10.74 42.88 2.90 5.05 9.10 44.03

Position Delta without Futures 3.00 3.71 7.79 28.43 2.76 4.70 6.92 31.57

Position Gamma 4.03 7.73 19.13 70.06 10.54 9.90 19.92 73.72

Position Vega 2.32 3.86 7.33 32.93 3.42 3.55 7.05 32.89

45

Table 10: Percentage of Trades in Each Moneyness Category

Table 10 presents the percentage of trades in each category of option moneyness for traders who trade in all

categories, where moneyness is defined by a 3% range. In other words, for a range of 3%, an at-the-money (ATM)

option is one whose strike price is within 3% of the price of the futures settlement price, an out-of-the-money

(OTM) option is one whose strike price is above 3% of the futures settlement price, and an in-the-money (ITM)

option is one whose strike price is below 3% of the futures settlement price.

Category Percentage of trades

OTM 66.17%

ATM 18.87%

ITM 14.12%